Wilshere has been immense for the Gunners since returning from a 15-month injury layoff, making 23 appearances in all competitions, and is viewed as a beacon of hope by many of the club's disillusioned fans.
But Thierry Henry, Cesc Fabregas and Alex Song have all swapped the Emirates Stadium for Camp Nou in recent seasons, and Alves believes the 21-year-old should make the same move if he is to fulfil his potential.
"He is a great player who we have met playing against Arsenal and without doubt he can reach the height of the players we have here at Barcelona like Xavi and Iniesta," Alves told reporters.
"He has a lot of quality and a great personality. If I was given the chance to choose, he is a player that I would sign for Barcelona."
Wilshere once again attracted wider international attention with a man-of-the-match showing as England surprisingly recorded a deserved 2-1 victory over Brazil earlier this month.
Alves believes an experimental team selection by new Selecao boss Luiz Felipe Scolari was a factor in the result, although he insists no excuses can be made for the defeat.
"England are a historic team which is not going through its finest period," he continued. "But coming up against a rival like this is always difficult.
"Excuses are not valid in this sport but we had players from Brazil who haven’t played much at all. Because of these circumstances, I think we did a good job. There were good and bad things."